Trigonometric Functions And Equations

If \(2 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=0\) has exactly 3 solutions in the interval \(\left[0, \frac{\mathrm{n} \pi}{2}\right], \mathrm{n} \in \mathrm{N}\), then the roots of the equation \(x^2+\mathrm{n} x+(\mathrm{n}-3)=0\) belong to :